Simplify the following expression: $r = \dfrac{9x^2 - 63x - 72}{x + 1} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ r =\dfrac{9(x^2 - 7x - 8)}{x + 1} $ Then we factor the remaining polynomial: $x^2 {-7}x {-8} $ ${1} {-8} = {-7}$ ${1} \times {-8} = {-8}$ $ (x + {1}) (x {-8}) $ This gives us a factored expression: $\dfrac{9(x + {1}) (x {-8})}{x + 1}$ We can divide the numerator and denominator by $(x - 1)$ on condition that $x \neq -1$ Therefore $r = 9(x - 8); x \neq -1$